Developing new tools in community detection and graph-based signal analysis

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In many settings, data naturally arise as connections between individual nodes in a graph (for example, friendship or collaboration networks in social media). Alternatively, data arising in other spaces (such as images) can be coerced into a graph-like structure for analysis, the suggested advantage being that one can unlock alternative information such as dependency structure not obvious in the original domain, or that network sparsity can be exploited for simpler analysis.The literature for modelling and analysing networks is now well-established via both of the approaches described above. However, there are still open questions in this research area which need to be addressed. For example, how can we build nodal or edge membership constraints into network-related analysis? Can transformation methods currently employed in analysing data arising on a graph (such as wavelets) be exploited for the analysis of static and dynamic networks? Could this result in more efficient tools, such as change-point techniques or online settings? Are there more robust ways of parameter estimation in the presence of missing data in statistical models for networks and their characterisation?The aim of this project is to present a range of potential problems arising in the general area of decision-making for network data. Specifically, we want to consider problems where there is a lack of, or unsatisfactory, methodological development of practical interest.